Broken lighting in Blender file
Have you played with the "Light Falloff" node?
Just add the node into your light material and try the different falloff types.
  

But you can go further if you play with math nodes. First you need to understand how to build them:

Constant falloff : same strength everywere, no matter if you're close or far from the emitter.
Linear falloff : strength decreasing with the distance (strength = 1/distance).
Quadratic falloff : same as linear but decreases faster (strength = 1/distance²).  

Now we can play with math nodes to get tweaks and lower strength values.

I'm using your file but I had to fix your plane (removed doubles and useless perpendicular face)